Answer
$\int(\sqrt x e^{\sqrt x})$
solution:
let,
$u=\sqrt x, du=1/(2\sqrt x)dx$
$2\int u^{2}*e^{u} du$
applying integration by parts:
$u^{2}*e^(u)-\int(e^(u)* 2u) du$
let,
$t = 2u$
$ds=e^(u)$
$dt = 2du$
$s= e^(u) du$
$\int(e^u*2u)$
Applying integration by parts
$2u*e^(u)-\int(2e^(u))$
$2ue^(u)-2e^(u) $-----(equation 2)
Work Step by Step
putting equation 2 in the main equation:
$2{u^(2)e^(u)-2ue^(u)+2e^(u)}$
$2e^(u)(u^(2)-2u+2)$
substituting $u = \sqrt x$
$2e^(\sqrt x)(x-2\sqrt x+2)+c$
